static void Test_FindMAxSubmatrix()
{
int[,] inMtrx = new int[6, 6] {
{ 2, -1, 2, -1, 4, -5 }, { 2, 8, 2, -1, 4, -5 }, { 2, -1, 2, -1, 4, -5 }, { 2, -1, 2, -1, 4, -5 }, { 2, -1, 2, -1, 4, -5 }, { -2, -1, -2, -1, 4, -5 }
};
MaxSubmatrix.PrintMatrix(inMtrx);
MaxSumMatrix mxMatrix = MaxSubmatrix.FindMaxSumSubmatrix(inMtrx);
Console.WriteLine("Max sum = {0}", mxMatrix.sum);
MaxSubmatrix.PrintMatrix(inMtrx, mxMatrix.rowStart, mxMatrix.rowEnd, mxMatrix.colStart, mxMatrix.colEnd);
// case 2
inMtrx = new int[, ] {
{ -1, -2, -3, -4 }, { -5, -6, -7, -8 }, { -9, -10, -11, -12 }, { -13, -14, -15, -16 }
};
MaxSubmatrix.PrintMatrix(inMtrx);
mxMatrix = MaxSubmatrix.FindMaxSumSubmatrix(inMtrx);
Console.WriteLine("Max sum = {0}", mxMatrix.sum);
MaxSubmatrix.PrintMatrix(inMtrx, mxMatrix.rowStart, mxMatrix.rowEnd, mxMatrix.colStart, mxMatrix.colEnd);
// case 3
inMtrx = new int[, ] {
{ 1, -61, 5126, 612, 6 },
{ 41, 6, 7, 2, -71 },
{ 73, -62, 678, 1, 7 },
{ -616136, 61, -83, 724, -151 },
{ 6247, 872, 2517, 8135, 1 }
};
MaxSubmatrix.PrintMatrix(inMtrx);
mxMatrix = MaxSubmatrix.FindMaxSumSubmatrix(inMtrx);
Console.WriteLine("Max sum = {0}", mxMatrix.sum);
MaxSubmatrix.PrintMatrix(inMtrx, mxMatrix.rowStart, mxMatrix.rowEnd, mxMatrix.colStart, mxMatrix.colEnd);
// case 4
inMtrx = new int[, ] {
{ 0, -2, -7, 0 },
{ 9, 2, -6, 2 },
{ -4, 1, -4, 1 },
{ -1, 8, 0, -2 }
};
MaxSubmatrix.PrintMatrix(inMtrx);
mxMatrix = MaxSubmatrix.FindMaxSumSubmatrix(inMtrx);
Console.WriteLine("Max sum = {0}", mxMatrix.sum);
MaxSubmatrix.PrintMatrix(inMtrx, mxMatrix.rowStart, mxMatrix.rowEnd, mxMatrix.colStart, mxMatrix.colEnd);
}
public static MaxSumMatrix FindMaxSumSubmatrix(int[,] inMtrx)
{
MaxSumMatrix maxSumMtrx = new MaxSumMatrix();
// Step 1. Create SumMatrix - do the cumulative columnar summation
// S[i,j] = S[i-1,j]+ inMtrx[i-1,j];
int m = inMtrx.GetUpperBound(0) + 2;
int n = inMtrx.GetUpperBound(1) + 1;
int[,] sumMatrix = new int[m, n];
for (int i = 1; i < m; i++)
{
for (int j = 0; j < n; j++)
{
sumMatrix[i, j] = sumMatrix[i - 1, j] + inMtrx[i - 1, j];
}
}
PrintMatrix(sumMatrix);
// Step 2. Create rowSpans starting each rowIdx. For these row spans, create a 1-D array r_ij
for (int x = 0; x < n; x++)
{
for (int y = x; y < n; y++)
{
int[] r_ij = new int[n];
for (int k = 0; k < n; k++)
{
r_ij[k] = sumMatrix[y + 1, k] - sumMatrix[x, k];
}
// Step 3. Find MaxSubarray of this r_ij. If the sum is greater than the last recorded sum =>
// capture Sum, colStartIdx, ColEndIdx.
// capture current x as rowTopIdx, y as rowBottomIdx.
MaxSum currMaxSum = KadanesAlgo.FindMaxSumSubarray(r_ij);
if (currMaxSum.maxSum > maxSumMtrx.sum)
{
maxSumMtrx.sum = currMaxSum.maxSum;
maxSumMtrx.colStart = currMaxSum.maxStartIdx;
maxSumMtrx.colEnd = currMaxSum.maxEndIdx;
maxSumMtrx.rowStart = x;
maxSumMtrx.rowEnd = y;
}
}
}
return(maxSumMtrx);
}
